{"id":"https://openalex.org/W2940356136","doi":"https://doi.org/10.1145/3302504.3313350","title":"Formal methods for computing hyperbolic invariant sets for nonlinear systems","display_name":"Formal methods for computing hyperbolic invariant sets for nonlinear systems","publication_year":2019,"publication_date":"2019-04-08","ids":{"openalex":"https://openalex.org/W2940356136","doi":"https://doi.org/10.1145/3302504.3313350","mag":"2940356136"},"language":"en","primary_location":{"id":"doi:10.1145/3302504.3313350","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3302504.3313350","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087306498","display_name":"Guillaume O. Berger","orcid":"https://orcid.org/0000-0002-0633-8948"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Guillaume O. Berger","raw_affiliation_strings":["UCLouvain, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056625594","display_name":"Rapha\u00ebl M. Jungers","orcid":"https://orcid.org/0000-0002-7789-0940"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Rapha\u00ebl M. Jungers","raw_affiliation_strings":["UCLouvain, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLouvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"260","last_page":"261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9563000202178955,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9563000202178955,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13286","display_name":"Modeling and Simulation Systems","score":0.9556999802589417,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9204000234603882,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6745887398719788},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5974285006523132},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.593515157699585},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5686095356941223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.565293550491333},{"id":"https://openalex.org/keywords/hyperbolic-coordinates","display_name":"Hyperbolic coordinates","score":0.5178311467170715},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.46813496947288513},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.4577871561050415},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.45567238330841064},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.4342668056488037},{"id":"https://openalex.org/keywords/hyperbolic-space","display_name":"Hyperbolic space","score":0.410084992647171},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40486863255500793},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3808520436286926},{"id":"https://openalex.org/keywords/hyperbolic-equilibrium-point","display_name":"Hyperbolic equilibrium point","score":0.36543214321136475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3321838974952698},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.32660022377967834}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6745887398719788},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5974285006523132},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.593515157699585},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5686095356941223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.565293550491333},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.5178311467170715},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.46813496947288513},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.4577871561050415},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.45567238330841064},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.4342668056488037},{"id":"https://openalex.org/C83677898","wikidata":"https://www.wikidata.org/wiki/Q1878538","display_name":"Hyperbolic space","level":2,"score":0.410084992647171},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40486863255500793},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3808520436286926},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.36543214321136475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3321838974952698},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.32660022377967834},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3302504.3313350","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3302504.3313350","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W219178713","https://openalex.org/W2577900305","https://openalex.org/W2776884190","https://openalex.org/W2962986757","https://openalex.org/W4205612902"],"related_works":["https://openalex.org/W4388640056","https://openalex.org/W4366330423","https://openalex.org/W3128228318","https://openalex.org/W4297783881","https://openalex.org/W1608408498","https://openalex.org/W2103057821","https://openalex.org/W2089251038","https://openalex.org/W2362866365","https://openalex.org/W2106320975","https://openalex.org/W3155748067"],"abstract_inverted_index":{"Hyperbolicity":[0],"is":[1,71,77,140,155],"a":[2,90,100,143,151],"cornerstone":[3],"of":[4,15,26,83,99,110,114,135],"nonlinear":[5],"systems":[6,31,49],"theory.":[7],"Hyperbolic":[8,29],"dynamics":[9],"are":[10],"characterized":[11],"by":[12],"the":[13,21,24,27,46,80,111,115,124,130,133,136,146,158],"presence":[14],"expanding":[16,125],"and":[17,54,117,126],"contracting":[18,127],"directions":[19,58,128],"for":[20,129,149],"derivative":[22,131],"along":[23,132],"trajectories":[25,134],"system.":[28,103,137],"dynamical":[30,102],"enjoy":[32],"many":[33,57],"interesting":[34],"properties":[35],"like":[36],"structural":[37],"stability,":[38],"ergodicity,":[39],"transitivity,":[40],"etc.":[41],"Since":[42],"their":[43],"introduction":[44],"in":[45,56],"1960's,":[47],"hyperbolic":[48,64,96,152],"have":[50],"been":[51],"intensively":[52],"studied":[53],"generalized":[55],"(e.g.,":[59],"partial":[60],"hyperbolicity,":[61,63],"nonuniform":[62],"control":[65],"theory,":[66],"etc.).":[67],"In":[68,85],"contrast,":[69],"it":[70],"surprising":[72],"to":[73,94,122],"see":[74],"how":[75],"few":[76],"known":[78],"about":[79],"algorithmic":[81],"verification":[82],"hyperbolicity.":[84],"this":[86],"poster,":[87],"we":[88],"describe":[89],"Hybrid":[91],"Systems":[92],"framework":[93],"compute":[95,123],"invariant":[97,153],"sets":[98],"given":[101],"The":[104,138],"method":[105,139],"relies":[106],"on":[107,118,142],"an":[108],"abstraction":[109],"state":[112],"space":[113],"system,":[116],"path-complete":[119],"'Lyapunov-like'":[120],"techniques":[121],"illustrated":[141],"numerical":[144],"example:":[145],"Ikeda":[147],"map":[148],"which":[150],"set":[154],"computed":[156],"using":[157],"framework.":[159]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
